CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt149",{id:"formSmash:upper:j_idt149",widgetVar:"widget_formSmash_upper_j_idt149",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt150_j_idt152",{id:"formSmash:upper:j_idt150:j_idt152",widgetVar:"widget_formSmash_upper_j_idt150_j_idt152",target:"formSmash:upper:j_idt150:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Homogenized Spectral Problems for exactly solvable operators:Asymptotics of polynomial eigenfunctionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2009 (English)In: Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, E-ISSN 1663-4926, Vol. 45, p. 525-568Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Kyoto,Japan, 2009. Vol. 45, p. 525-568
##### Keywords [en]

differential equations, subharmonic functions
##### National Category

Natural Sciences
##### Identifiers

URN: urn:nbn:se:su:diva-33667DOI: 10.2977/prims/1241553129ISI: 000270167800008OAI: oai:DiVA.org:su-33667DiVA, id: diva2:283352
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt459",{id:"formSmash:j_idt459",widgetVar:"widget_formSmash_j_idt459",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt470",{id:"formSmash:j_idt470",widgetVar:"widget_formSmash_j_idt470",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true}); Available from: 2011-01-05 Created: 2009-12-23 Last updated: 2017-12-12Bibliographically approved

Consider a homogenized spectral pencil of exactly solvable linear differential operators T-lambda = Sigma(k)(i=0) Q(i)(z)lambda(k-i) d(i)/dz(i), where each Q(i)(z) is a polynomial of degree at most i and lambda is the spectral parameter. We show that under mild nondegeneracy assumptions for all sufficiently large positive integers n there exist exactly k distinct values lambda(n,j), 1 <= j <= k, of the spectral parameter lambda such that the operator T-lambda has a polynomial eigenfunction p(n,j)(z) of degree n. These eigenfunctions split into k different families according to the asymptotic behavior of their eigenvalues. We conjecture and prove sequential versions of three fundamental properties: the limits Psi(j)(Z) = lim(n ->infinity) P'(n,j) (z)/lambda(n,j)p(n,j)(z) exist, are analytic and satisfy the algebraic equation Sigma(k)(i=0)Q(i)(z)Psi(i)(j)(z) = 0 almost everywhere in CP1. As a consequence we obtain a class of algebraic functions possessing a branch near infinity is an element of CP1 which is representable as the Cauchy transform of a compactly supported probability measure.

doi
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1295",{id:"formSmash:j_idt1295",widgetVar:"widget_formSmash_j_idt1295",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1348",{id:"formSmash:lower:j_idt1348",widgetVar:"widget_formSmash_lower_j_idt1348",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1349_j_idt1351",{id:"formSmash:lower:j_idt1349:j_idt1351",widgetVar:"widget_formSmash_lower_j_idt1349_j_idt1351",target:"formSmash:lower:j_idt1349:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});